The term optics includes semi-finished lens blanks, monofocal or multifocal lenses, and finished optical lenses incorporating a wide variety of known lens designs. An optic such as a progressive addition lens is preferred to a bifocal optic because the progressive addition optic provides a channel in which the add power changes continuously while adding only a relatively small level of astigmatism, so that the quality of the image formed by the transition zone remains acceptable. In addition, the front surface of the progressive addition optic remains continuous and smooth, causing the transition zone to remain substantially invisible. This continuous transition from one sagital radius of curvature to a smaller radius inevitably introduces a difference between the sagital to the tangential radii of curvature, which appears as unwanted astigmatism. In order to have a successful progressive addition optical design, it is important to minimize the unwanted astigmatism along the central meridional line which connects the major reference point to the center of the add power zone. Previously, this problem has been approached analytically and by application of finite element analysis. Progressive designs embodying one or more umbilical lines have been proposed. Splines as well as conic sections have been applied to model the surface geometry. Current designs of progressive addition optics contain the deficiencies inherent in the selected design methodology, i.e., a narrow progressive addition channel in which unwanted astigmatism is held to less than 0.25 D, appearance of unwanted astigmatism in the periphery of the optic which reduces the field of view, existence of refractive errors, etc.
Refractive index gradients have previously been used in order to develop a transition of spherical power. For example, Guilino (U.S. Pat. Nos. 4,240,719, 5,148,205 and 5,042,936), in a process uniquely applicable to mineral glass, discloses forming continuous refractive gradients (n=f{z}) to construct a continuous progressive addition surface in which the gradient is introduced by means of ion implantation or exposure of the optic to a solution capable of diffusing heavy ions into the material of the optic. Guilino demonstrated that it is possible to reduce the difference between the sagital and tangential radii of curvatures while varying the rate of change of the sagital radius of curvature by introducing an additional function which controls the variation of refractive index sagitally. However, unwanted astigmatism is not eliminated and refractive errors develop at relatively low values of the angle of vision because the design of the refractive gradient, as well as the process of achieving the refractive index gradient, yields plane surfaces of constant refractive indices (i.e., n(z)=f(z)) in order to achieve a continuous surface with continuous first and second derivatives with respect to the sagital depth.